You could change it so that Barnes doesn't summon an actual copy of the minion, but a fixed Barnes token 1/1 that copies its effects. Something like a Mirage that assumes the effects of whatever Barnes chooses. The Mirage will then do whatever the original could do (active effects, end of turn effects, deathrattles etc.) but it will always be a flat 1/1. If you silence it, it's still a 1/1. If you resurrect it, it's a blank 1/1 with no effects.
You could change it so that Barnes doesn't summon an actual copy of the minion, but a fixed Barnes token 1/1 that copies its effects. Something like a Mirage that assumes the effects of whatever Barnes chooses. The Mirage will then do whatever the original could do (active effects, end of turn effects, deathrattles etc.) but it will always be a flat 1/1. If you silence it, it's still a 1/1. If you resurrect it, it's a blank 1/1 with no effects.
Why not just make Barnes more expensive and adjust the stats accordingly so it doesn't happen so early?
Make him a 6 mana 5/6 maybe?